Towards spaces of harmonic functions with traces in square Campanato spaces and their scaling invariants
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Bibliographic record
Abstract
For [Formula: see text] and [Formula: see text], let [Formula: see text] be the space of harmonic functions [Formula: see text] on the upper half-space [Formula: see text] satisfying [Formula: see text] and [Formula: see text] be the Campanato space on [Formula: see text]. We show that [Formula: see text] coincides with [Formula: see text] for all [Formula: see text], where the case [Formula: see text] was originally discovered by Fabes, Johnson and Neri [E. B. Fabes, R. L. Johnson and U. Neri, Spaces of harmonic functions representable by Poisson integrals of functions in BMO and [Formula: see text], Indiana Univ. Math. J. 25 (1976) 159–170] and yet the case [Formula: see text] was left open. Moreover, for the scaling invariant version of [Formula: see text], [Formula: see text], which comprises all harmonic functions [Formula: see text] on [Formula: see text] satisfying [Formula: see text] we show that [Formula: see text], where [Formula: see text] is the collection of all functions [Formula: see text] such that [Formula: see text] are in [Formula: see text]. Analogues for solutions to the heat equation are also established. As an application, we show that the spaces [Formula: see text] unify naturally [Formula: see text], [Formula: see text] and [Formula: see text] which can be effectively adapted and applicable to suit handling the well/ill-posedness of the incompressible Navier–Stokes system on [Formula: see text].
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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